3a^2-12a-64=0

Solution for 3a^2-12a-64=0 equation:

3a^2-12a-64=0

a = 3; b = -12; c = -64;
Δ = b2-4ac
Δ = -122-4·3·(-64)
Δ = 912
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{57}}{2*3}=\frac{12-4\sqrt{57}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{57}}{2*3}=\frac{12+4\sqrt{57}}{6}
$